A friend of mine asked me to talk about the links Google sometimes drops on its homepage. Just after the Superbowl, for instance, Google.com hosted a prominent link to a YouTube video channel with all the ads. My friend asked, given the enormous PageRank of Google.com, why didn't that Youtube channel page show up in the rankings of a search for "superbowl?"
A good question, because one of the key factors in ranking is the quality of links coming in to your site. But quality is measured along several dimensions, and that is the first part of the answer to the question. Google doesn't like links that are ads or otherwise not 'natural' links. They must be keenly aware that their own homepage is a screaming example of purely artifical links. They're temporary, promotional links probably placed by an internal advertising team. (In this case, advertising another Google product, even!) So while the link is on a high PageRank page, Google discounts it because of its commercial, artificial nature.
Some other thoughts about Google: They doesn't index their own homepage daily. A quick look at the Google cache from my IP shows the Feb 3rd page, right now -- almost a week later. So they're only crawling their own site once a week or so, and different datacenters store different cache dates. (As shown by my friend's cache query -- run before mine, and showing a more recent cache date...) And they seem to be running host detection on their site, as evidenced by the various ads and popups that will appear depending on which browser you visit them with, where you visit them from, etc. So Googlebot might not trigger the ads consistently anyway. All just more reasons for Google to ignore its own promotional links.
However, even if that link did count for quite a bit, it's still only one link. If I were ever asked what my ideal link would be, I'd say that it would be one that was so compelling, lots and lots of people would want to put it on their own sites, too. Any single link -- even The Perfect Link with great anchor text and on a 10 PageRank page -- is just one link. Google tries to be a democracy, and so while they do have to weight links, they don't want that weighting overriding the importance of multiple links as a better indicator. So the ideal link would be part of a contest or something, formatted just as you described, but then with a chance for payoff in the end. Tied to something that's not directly the link -- maybe create a "Fans of MySite" club, and say that one lucky fan will win a new car at the end of the month. To be a fan, of course, all you have to do is host this link... :o)
So, there's my thoughts about the matter. For whatever they're worth. (Not even the paper they're printed on!) (Ha ha...)